Factoring Trinomials
If a trinomial ax +
bx + c will not factor by any other method, use trial and error
to fit it into the F O I L pattern:
1. Set up empty parentheses:  .
If a,b,c are positive, then both signs are positive  .
If b is negative but c is positive, then both signs are
negative  .
If c is negative, then one sign is positive and the other is
negative  .
2. Try the factors of a in front positions  , and the factors of c in the back positions  , until the resulting product is the orginal
trinomial.
Example: factor 2x
- x - 10
step 1:
step 2:
step 3: The factors of 2 are 2 and 1; the factors of 10 are 10
and 1 or 5 and 2:
(2x + 10)(x - 1) = 2x
+ 8x - 10
(2x + 5)(x - 2) = 2x+
x - 10
The second trial is almost correct; only the sign of the
middle term is wrong. So we change signs:
(2x - 5)(x + 2) = 2x-
x - 10
The answer is (2x - 5)(x + 2) .
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